For example, Japanese Patent Application Laid-Open (kokai) No. 2004-183585 discloses a conventional air-fuel-ratio control apparatus of such a type. In the disclosed air-fuel-ratio control apparatus for an internal combustion engine (hereinafter sometimes simply referred to as “engine”), a composite air-fuel ratio is obtained, which is a value on the basis of the sum of the out put value the upstream air-fuel-ratio sensor and downstream-side feedback correction value that is calculated based upon (through proportional plus integral plus derivative processing (PID processing) of) a deviation, from a predetermined downstream-side target value, of the output value of the downstream air-fuel-ratio sensor. An upstream-side feedback correction value is calculated on the basis of (through proportional plus integral processing (PI processing) of a deviation) the value corresponding to the deviation of the composite air-fuel ratio from the target air-fuel ratio (the deviation of the cylinder fuel supply quantity, which is obtained by dividing a cylinder intake air quantity by the composite air-fuel ratio, from the target cylinder fuel supply quantity, which is obtained by dividing the cylinder intake air quantity by the target air-fuel ratio). A fuel injection quantity is calculated on the basis of the upstream-side feedback correction value and a base fuel injection quantity, which is a quantity of fuel acquired based upon the operation state of the engine for obtaining the target air-fuel ratio. The instruction for injecting the fuel in the fuel injection quantity is given to an injector, whereby the air-fuel ratio is feedback-controlled.
Meanwhile, a fluctuation may be produced in the downstream-side feedback correction value due to the influence of disturbance or the like. In this case, as shown in FIG. 17, the fluctuation produced in the downstream-side feedback correction value is transmitted as the fluctuation of the composite air-fuel ratio obtained on the basis of the downstream-side feedback correction value, and the fluctuation of the composite air-fuel ratio is transmitted to the upstream-side feedback correction value.
When the fluctuation is transmitted to the upstream-side feedback correction value, the fluctuation is also transmitted to the fuel injection quantity calculated based upon the upstream-side feedback correction value. When the fluctuation is transmitted to the fuel injection quantity, the fluctuation is also transmitted to the air-fuel ratio (i.e., air-fuel ratio of exhaust gas) that is based upon the fuel injection quantity. Accordingly, the fluctuation is transmitted to the output value from the upstream-side sensor and the output value from the downstream-side sensor. As a result, the fluctuation is transmitted to the downstream-side feedback correction value that is based upon the output value from the downstream air-fuel-ratio sensor. A series of flow of transmitting the fluctuation in this manner is referred to as “transmission loop of fluctuation”.
Since the composite air-fuel ratio is the value based upon the sum of the output value from the upstream air-fuel-ratio sensor and the downstream-side feedback correction value as described above, the fluctuation of the composite air-fuel ratio can be increased more than the fluctuation of the output value from the upstream air-fuel-ratio sensor. Therefore, when the “transmission loop of fluctuation” is repeated, the fluctuation produced in the upstream-side feedback correction value that is calculated on the basis of the composite air-fuel ratio gradually increases, resulting in entailing a problem of the increase in the fluctuation of the air-fuel ratio.